Dance Of The Spaghetti

When we cook spaghetti, noodles loosen up as they take on water, and undergo a beautiful choreography driven by the thermal energy of the boiling water. Although they become more flexible, they still maintain some structure, i.e. they are smooth curves.

We can make a crude model of the spaghetti noodle as a chain of $$N$$ short rods of length $$\delta l$$ that are connected end to end, but otherwise free to rotate about the connections. Under these assumptions, calculate the root mean squared distance (in $$\si{\centi\meter}$$) between the ends of the noodle (i.e. the blue and red balls in the diagram) as it dances in the pot.

Details and Assumptions:

• $$\delta l = 1 \si{\milli\meter}$$.
• $$N = 350$$.
• Ignore the nasty issue of the fact that spaghetti cannot pass through itself.
• Assume the spaghetti is alone in the pot ​and doesn't interact with the walls.
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